Propagate

Propagate table and series representations

ndmap.propagate.identity(order: tuple[int, ...], point: list[torch.Tensor], *, flag: bool = False, parametric: list | None = None, jacobian: Callable | None = None) → list | dict[tuple[int, ...], torch.Tensor][source]

Generate identity derivative table or identity series

Note, identity table or series represent an identity mapping

Parameters:

order (tuple[int, ...], non-negative) – maximum derivative orders
point (Point) – evaluation point
flag (bool, default=False) – flag to return identity series instead of table
parametric (Optional[Table]) – optional parametric table
jacobian (Optional[Callable]) – torch.func.jacfwd (default) or torch.func.jacrev

Returns:

identity derivative table or series

Return type:

Union[Table, Series]

Examples

>>> import torch
>>> state = torch.tensor([0.0, 0.0])
>>> knobs = [torch.tensor([0.0, 0.0])]
>>> point = [state, *knobs]
>>> identity((1, 1), point)
[[tensor([0., 0.]),
tensor([[0., 0.],
        [0., 0.]])],
[tensor([[1., 0.],
        [0., 1.]]),
tensor([[[0., 0.],
        [0., 0.]],

[[0., 0.], [0., 0.]]])]]

>>> identity((1, 1), point, flag=True)
{(0, 0, 0, 0): tensor([0., 0.]),
(0, 0, 1, 0): tensor([0., 0.]),
(0, 0, 0, 1): tensor([0., 0.]),
(1, 0, 0, 0): tensor([1., 0.]),
(0, 1, 0, 0): tensor([0., 1.]),
(1, 0, 1, 0): tensor([0., 0.]),
(1, 0, 0, 1): tensor([0., 0.]),
(0, 1, 1, 0): tensor([0., 0.]),
(0, 1, 0, 1): tensor([0., 0.])}

ndmap.propagate.propagate(dimension: tuple[int, ...], order: tuple[int, ...], data: list, knobs: list[torch.Tensor], table: list, *, intermediate: bool = True, jacobian: Callable | None = None) → list | torch.Tensor

Propagate derivative table representation through a given table

Note, can be used for composition of deririvative tables Composition should be performed for tables that map zero state to zero Also, tables are expected to have identical knobs

Parameters:

dimension (tuple[int, ...], positive) – dimensions
order (tuple[int, ...], non-negative) – maximum derivative orders
data (Table) – input derivative table
knobs (Knobs) – input parametric variables
table (Table) – input table mapping approximation
intermediate (bool, default=True) – flag to return intermediate derivatives
jacobian (Optional[Callable]) – torch.func.jacfwd (default) or torch.func.jacrev

Return type:

Union[Table, Tensor]

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> from ndmap.evaluate import compare
>>> def fn(x, l): q, p = x; return torch.stack([q + l*p, p])
>>> x = torch.tensor([0.0, 0.0], dtype=torch.float64)
>>> t = derivative(1, fn, x, 0.5)
>>> compare(derivative(1, fn, x, 1.0), propagate((2, ), (1, ), t, [], t))
True